Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON3):

Solution:
n,m=map(int,input().split())
M=[list(map(int,input().split())) for i in range(n)]
M1=[[0]*m for i in range(n)]

for i in range(n) :
    for j in range(m) :
        M1[i][j]=M[i][j]
l=[]
l1=[]
c=0
for i in range(n) :
    V=min(M[i])
    if n>m :
        c=1
        break
    for j in range(V) :
        l.append(['row',i+1])
    for j in range(m) :
        M[i][j]=M[i][j]-V
    for j in range(m) :
        V=M[i][j]
        for j1 in range(V) :
            l.append(['col',j+1])
        for j1 in range(n) :
            M[j1][j]=M[j1][j]-V
for i in range(n) :
    if c==1 :
        break
    if M[i].count(0)!=m :
        print(-1)
        exit()
if n<=m :
    print(len(l))
    for i in range(len(l)) :
        print(*l[i])
    exit()
for i in range(m) :
    ma=100000
    for j in range(n) :
        if ma>M1[j][i] :
            ma=M1[j][i]
    for j in range(ma) :
        l1.append(['col',i+1])
    for j in range(n) :
        M1[j][i]=M1[j][i]-ma
    for j in range(n) :
        V=M1[j][i]
        for j1 in range(V) :
            l1.append(['row',j+1])
        for j1 in range(m) :
            M1[j][j1]=M1[j][j1]-V
            

for i in range(n) :
    if M1[i].count(0)!=m:
        print(-1)
        exit()

print(len(l1))
for i in range(len(l1)) :
    print(*l1[i])